I think as long as you make sure that the company is a trusted one, private tours are a great way to know more about a certain country or place. I'm not certain but maybe it's about 4000 dollars per person for a private tour, don't quote me on this one, lol. The good thing about private tours is that they are personalised according to your preference. Here are a few private tour company I know of:

1. Cox and Kings. Probably the best when it comes to private tours since they are the oldest travel agency in India.
2. Greaves. Offers either affordable or expensive packages, you can choose which one you like.
3. Wild Frontiers. Offers tours mainly in the villages of India. Great for exploring unknown locations.